SECTION 1.3 PLANS FOR COLLECTION AND ANALYSIS OF DATA nt
Lo o IONI ———<———

Section 1.4. Overall and Dalal (1965) have described a procedure for
maximizing the power of a research methodology relative to cost through
the optimum allocation of resources to subjects; it reguires a priori esti-
mates of a number of design parameters. A procedure is described in
Section 4.5 for estimating the number of subjects reguired for an experi-
ment, one that does not necessitate making an estimate of the population
error variance.

1.4 OVERVIEW OF TYPES OF
EXPERIMENTAL DESIGNS

One of the procedures suggested above for increasing the power
of a research methodology was to employ a more sensitive experimental
design. In this context, the term experimental design refers to the plan by
which subjects are assigned to treatment levels and the data analyzed.

An almost bewildering array of kinds of experimental designs exists.
Fortunately, most complex experimental designs represent a combination
of a relatively small number of basic building block designs. For example.
most complex designs can be constructed by combining: two or more
completely randomized, randomized block, or Latin sguare designs. A
simple classification of the experimental designs described in this book is
outlined in Table 1.4-1. A more complete classification system appears in
Cox (1943); Doxtator, Tolman, Cormany, Bush, and Jensen (1942); and
Federer (1955, 6—12).

The category systematic designs in the outline is of historical interest
only. According to Leonard and Clark (1939), agricultural field research
employing systematic designs on a practical scale dates back to 1834.
Prior to the work of Fisher, as well as of Neyman and Pearson on the
theory of statistical inference, investigators used systematic schemes
rather than randomization procedures for assigning treatment levels to
plots of land or other suitable experimental units—hence the designation
systematic designs for these early field experiments. Impetus for this
early experimental research came from a need to improve agricultural
technigues. Today the nomenclature of experimental design is replete
with terms from agriculture. Systematic designs in which the randomization
principle is not followed do not provide a valid estimate of error variance
and hence are not subject to powerful tools of statistical analysis, such as
analysis of variance.

Modern principles of experimental design, particularly the principle
of random assignment of treatment levels to experimental units, received
general acceptance as a result of Fisher's work (1922, 1923, 1935). Experi-
mental designs using the randomization principle are called randomized
designs. Randomized designs can be subdivided into two distinct categories,
complete block designs and incomplete block designs, and two pseudo-